Phase space methods for non-linear analysis of pedalling forces in cycling

Introduction: From the perspective of dynamic systems theory, stability and variability of biological signals are both understood as a functional adaptation to variable environmental conditions. In the present study, we examined whether this theoretical perspective is applicable to the pedalling movement in cycling. Non-linear measures were applied to analyse pedalling forces with varying levels of subjective load. Materials and methods: Ten subjects completed a 13-sector virtual terrain profile of 15 km total length on a roller trainer with varying degrees of virtual terrain inclination (resistance). The test was repeated two times with different instructions on how to alter the bikes gearing. During the experiment, pedalling force and heart rate were measured. Force-time curves were sequenced into single cycles, linearly interpolated in the time domain, and z-score normalised. The established time series was transferred into a two-dimensional phase space with limit cycle properties given the applied 25% phase shift. Different representations of the phase space attractor were calculated within each sector and used as non-linear measures assessing pedalling forces. Results and discussion: A contrast analysis showed that changes in pedalling load were strongly associated to changes in non-linear phase space attractor variables. For the subjects investigated in this study, this association was stronger than that between heart rate and resistance level. The results indicate systematic changes of the pedalling movement as an adaptive response to an externally determined increase in workload. Future research may utilise the findings from this study to investigate possible relationships between subjective measures of exhaustion, comfort, and discomfort with biomechanic characteristics of the pedalling movement and to evaluate connections with dynamic stability measures.